At the moment, closing books in QuickBooks Self-Employed (QBSE) is not an option as it doesn't have a Chart of Accounts to record balances. As a result, you can continue using it as it is without closing it. The system will separate them when you pull up the reports and choose the period you want to view.
We recognize that each company has unique needs, and I can see how the feature you're looking for would benefit and empower your business. I recommend sending this request straight to our product engineers through feedback. It helps us improve the features of the program.